I'll try to answer your question now.

Zoc = V/I

similarly, Zsc = V/I

then Characteristic impedance, Zc = sqrt(Zoc*Zsc)

How can you get phase angle with this???

Keep in mind, that impedance in general, Z, is complex. And so according to the equation:

Z = V/I, it is required that in general, V or I or both are also complex.

 

For a newbie, explain what you mean by complex.
Complex usually means complicated.

 

This should be a sticky. It comes up time and again.
Someone should go over this thread and summarize the questions and answers, re

characteristic impedance
transmission lines
coax cables
mismatch
reflections
freespace
centre fed, dipoles
end fed antennas

That would be a poisoned chalice to take up. The drafting of said sticky would require the writer to negotiate a minefield of myth & fact.

 

No only the magnitude is obtained. In the expt, the p.d V across the transmission line model is measured and the current I at the line input is also obtained. Thus the short-circuit (or open circuit) impedance is obtained as follows:

Zoc = V/I

similarly, Zsc = V/I

then Characteristic impedance, Zc = sqrt(Zoc*Zsc)

How can you get phase angle with this???

On the web page you referenced:

http://home.mira.net/~marcop/ciocahalf.htm

near the bottom of the page under the heading "Notes", you will find this sentence:

"The Zoc and Zsc measurements both have magnitude and phase, so the Zo determined by Equation 6 will also have magnitude and phase."

You just didn't measure the phase of Zoc and Zsc as part of your experiment, but they have phase nonetheless.

 

But there is still one thing...
According to theory, the characteristic impedance should remain constant for high frequencies since it obeys this equation:

Zc = sqrt(L/C)

whereby L = inductance and C = capacitance and

L and C are independent of frequency

So why does Zc increase at high frequencies?? It should have been constant, right?

I was thinking that L might be increasing with frequency but theoretically this is not the case!!!! So what possible explanation can there be for this behaviour????

I don't think this is experimental error...

Your measurements were made on a network of R, L and C, not a real transmission line. Such a "lumped constant model" doesn't behave like a real transmission line at high frequencies, so you can't draw conclusions about real transmission line behavior at high frequencies from such models.

 

The sort of measurements you made in the lab can be made automatically with an instrument called an impedance analyzer. This device can measure the impedance across a pair of terminals at a large number of frequencies and then plot those measurements in graphical form. The impedance measured consists of a real and imaginary part, and can be displayed in magnitude and phase angle form, or as the real and imaginary parts.

Here are some plots of the impedance at one end of a 100 foot length of ordinary household telephone cable (just a twisted pair). The frequency is swept from 50 Hz to 5 MHz. The plots are on logarithmic horizontal (frequency axis) and a log vertical axis for the impedance magnitude, but linear vertical axis for the phase.

The green curve is the impedance magnitude from 1 ohm at the bottom to 10k ohms at the top. The yellow curve is the phase angle, from -100 degrees at the bottom to +100 degrees at the top.

In this sweep, the cable is open at the far end, away from the measurement terminals. The phase angle curve should make very sharp transitions from -90 degrees to +90 degrees, but the transition is not very rapid due to the losses in the cable. Also, in an ideal cable, the maximum impedance would be infinity, and the minimum would be zero. We see that for this real cable, the maximum impedance is about 1000 ohms, and the minimum is about 10 ohms:

In this sweep the cable is shorted at the far end:

In this sweep the plots for the open case, and for the shorted case are superimposed:

A property of logarithmic plots is that if you have two curves on the same graph, representing two measurements at each frequency, the point halfway between the two curves at a given frequency has the value SQRT(P1*P2), where P1 and P2 are the values of each curve at a single frequency. Since the two curves in this last plot are the data points of Zoc and Zsc, a curve drawn halfway between the two curves will be the magnitude of the characteristic impedance of the cable. As can be seen, it's very close to 100 ohms, and remains constant once you get above a few hundred kHz all the way up to 5 MHz.

 

Here's a plot of the same cable plotted on a log frequency scale. Notice how the impedance magnitude now can be seen to increase at lower and lower frequencies. I changed the maximum of the magnitude at the top of the plot to 1 megohm, and the impedance is still climbing as the frequency goes below 50 Hz.

Here's a plot of the cable, but with the maximum frequency of the sweep limited to 10 kHz, and with a linear vertical scale as well as a linear frequency scale. Now this plot looks like your plot.

 

What will be the variation (if any) in the characteristic impedance if the length of the transmission line used is varied?

 

Here's a plot of the cable, but with the maximum frequency of the sweep limited to 10 kHz, and with a linear vertical scale as well as a linear frequency scale. Now this plot looks like your plot.

The Electrician, have a look at these graphs (see attachment).

It gives a comparison between different line models.

Ideally, Zc does not change with length. So the 5km and the 0.2 km lines should have produced almost identical graphs. But it is quite different in my case! Can you please give an explanation?

For the last graph (blue one), where diameter has been increased, i think the variation is correct. This is because characteristic impedance also follow this relationship:

Zc = (276/sqrt(K))log (d/r)

where r is conductor radius and d is distance between conductor centres.

Hence when diameter (or radius) is increased from 0.4 mm to 0.9 mm, the graph shift downwards. Am i correct?

 

Hard to tell without a schematic of your network..

 

Hard to tell without a schematic of your network..

here is a representation of the circuit i used for the expt and the formula i used to calculate Zc.

The transmission line model is an equivalent network of resistors, capacitors and inductors.

3 different line models were used (see the graph for lengths and diameters)

 

The relevant parameter in the formula you posted in post #29 is d/r; that is, the impedance depends on the ratio of the diameters (or radii) or the inner conductor and outer conductor.

It is possible to have two coax lines with the same overall outside diameters, but with different inner conductor diameters. Those two lines will then have different characteristic impedances.

When you talk of "diameter" without specifying whether you mean overall outside cable diameter, or maybe inner conductor diameter, you are being imprecise. To just say that a cable has a "diameter", without more information (the ratio d/r is needed) is not enough to determine the characteristic impedance.

Suppose you wished to use your model to represent two different cables, with different d/r ratios. How would you adjust the parameters of your model to account for the different d/r ratios?